Complexes of differential forms and singularities: The injectivity theorem

In this paper, it is proved, that for varieties with (m-1)-Du Bois singularities, the natural morphism from the Grothendieck dual of the m-th graded Du Bois complex to the Grothendieck dual of its zero-th cohomology sheaf is injective on cohomology. This confirms Conjecture G of Popa, Shen, and Vo [PSV24].

💡 Research Summary

The paper “Complexes of differential forms and singularities: The injectivity theorem” establishes a long‑standing conjecture (Conjecture G of Popa, Shen, and Vo, 2024) concerning higher Du Bois singularities. The main result asserts that for a complex variety (X) over (\mathbb{C}) with pre‑((m!-!1))-Du Bois singularities, the natural morphism
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